Humans can now construct and piece together DNA sequences in order to design new biological systems and organisms. We can do this more quickly and less expensively than ever. Applications abound for our synthetic biological constructs, from sensors of biochemical and chemical weapons, to devices that will remove environmental pollutants, to gene therapies. Synthetic biology is the discipline that focuses on the construction of these novel biological systems. It has all the characteristic features of an engineering discipline: applying technical and scientific knowledge to design and implement devices, systems, and processes that safely realize a desired objective. Mathematical modeling has always been an important component of engineering disciplines. It can play an important role in synthetic biology the same way modeling helps in aircraft or architecture design: models and computer simulations can quickly provide a clear picture of how different components influence the behavior of the whole, reaching objectives quickly. The proposed activities will result in modeling tools that will help scientists and engineers to construct complex synthetic biological systems. These tools will be standardized, so that they are applicable to any synthetic biological system. The activities will also produce novel synthetic gene regulatory networks that can find applications in pharmaceutical production and gene therapies. We will develop sophisticated mathematical models of synthetic biological systems that connect the targeted biological phenotype (what we want the synthetic biological system to do) to the DNA sequence (that we need to physically construct to realize the synthetic biological system). We will conduct simulations of many alternate designs to decide on the optimum set of molecular components, before we go into the wet laboratory. We will then construct these designs in E. coli and optimize them for performance. We propose to work with synthetic tetracycline inducible networks because they have significant biomedical applications, mainly as gene therapy expression vectors. Tetracycline is a small antibiotic molecule that can safely turn on the production of any protein, when this protein is expressed under the control of a tetracycline-responsive DNA promoter. We will model, design, build and test these promoters to determine how to best control protein expression with tetracycline induction.